Type inference of singular matches on GADTs

[Simon Peyton Jones]

I haven't thought about how to implement such a thing. At the least, it would probably require some annotation saying that we expect `\HNil -> ()` to be exhaustive (as GHC won't, in general, make that assumption). Even with that, could we get type inference to behave? Possibly.

As I wrote in another post on this thread, it’s a bit tricky.

What would you expect of (EX1)

   \x -> case x of HNil -> blah

Here the lambda and the case are separated

Now (EX2)

\x -> (x, case x of HNil -> blah)

Here the lambda and the case are separated more, and x is used twice.
What if there are more data constructors that share a common return type? (EX3)


data HL2 a where

HNil1 :: HL2 []

HNil2 :: HL2 []

HCons :: …blah…

\x -> case x of { HNil1 -> blah; HNil 2 -> blah  }

Here HNil1 and HNil2 both return HL2 [].   Is that “singular”?

What if one was a bit more general than the other?   Do we seek the least common generalisation of the alternatives given? (EX4)

data HL3 a where

HNil1 :: HL2 [Int]

HNil2 :: HL2 [a]

HCons :: …blah…

\x -> case x of { HNil1 -> blah; HNil 2 -> blah  }

What if the cases were incompatible?  (EX5)

data HL4 a where

HNil1 :: HL2 [Int]

HNil2 :: HL2 [Bool]

HCons :: …blah…

\x -> case x of { HNil1 -> blah; HNil 2 -> blah  }

Would you expect that to somehow generalise to `HL4 [a] -> blah`?

What if x matched multiple times, perhaps on different constructors (EX6)

\x -> (case s of HNil1 -> blah1;  case x of HNil2 -> blah)


The water gets deep quickly here.  I don’t (yet) see an obviously-satisfying design point that isn’t massively ad-hoc.

Simon


From: ghc-devs <ghc-devs-bounces at haskell.org> On Behalf Of Richard Eisenberg
Sent: 29 March 2021 03:18
To: Alexis King <lexi.lambda at gmail.com>
Cc: ghc-devs at haskell.org
Subject: Re: Type inference of singular matches on GADTs




On Mar 26, 2021, at 8:41 PM, Alexis King <lexi.lambda at gmail.com<mailto:lexi.lambda at gmail.com>> wrote:

If there’s a single principal type that makes my function well-typed and exhaustive, I’d really like GHC to pick it.

I think this is the key part of Alexis's plea: that the type checker take into account exhaustivity in choosing how to proceed.

Another way to think about this:

f1 :: HList '[] -> ()
f1 HNil = ()

f2 :: HList as -> ()
f2 HNil = ()

Both f1 and f2 are well typed definitions. In any usage site where both are well-typed, they will behave the same. Yet f1 is exhaustive while f2 is not. This isn't really about an open-world assumption or the possibility of extra cases -- it has to do with what the runtime behaviors of the two functions are. f1 never fails, while f2 must check a constructor tag and perhaps throw an exception.

If we just see \HNil -> (), Alexis seems to be suggesting we prefer the f1 interpretation over the f2 interpretation. Why? Because f1 is exhaustive, and when we can choose an exhaustive interpretation, that's probably a good idea to pursue.

I haven't thought about how to implement such a thing. At the least, it would probably require some annotation saying that we expect `\HNil -> ()` to be exhaustive (as GHC won't, in general, make that assumption). Even with that, could we get type inference to behave? Possibly.

But first: does this match your understanding?

Richard
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